### 1. Introduction

*Ralstonia eutropha*. The validation of simulated CFD model was carried with the help of experimental data available in the literature for biodegradation [14]. Habibi et al. [15] experimented in plug flow PBR under semi pilot-scale to evaluate FA degradation process in continuous mode of operation. In this study,

*Ralstonia eutropha*was immobilized on polyurethane foam, and the inlet concentration of FA was increased stepwise. The experimental data was successfully simulated with a CFD model where a biochemical reaction was combined with fluid dynamics [15]. In our previous manuscript [16], biodegradation of 4-CP was studied in a batch process using

*Bacillus subtilis*MF447840.1, which can able to degrade 4-CP with the concentration of 1 g/L within 40 h. As per our knowledge concern, there are few studies reported on the prediction of hydrodynamics properties for biodegradation of 4-CP using CFD analysis, therefore, the prospective importance of these properties on 4-CP biodegradation in PBR has been emphasized by experiments with

*B. subtilis MF447840.1.*

*B. subtilis MF447840.1*immobilized bead for biodegradation of 4-CP in the synthetic wastewater. The optimum process parameters so obtained from CFD simulation was employed for validation.

### 2. Material and Methods

### 2.1. Chemicals

### 2.2. Microorganism and Seed Culture

*B. subtilis MF447840.1*employed in the present investigation was purified from the water collected from drain of service center for Hyundai car, Agartala, India, and characterized [16]. The pure culture was inoculated in fifty milliliter media by the help of platinium loop and kept at 37°C in a shaker at 150 rpm. The media was composed of ammonium nitrate, 0.5 g/L; magnesium sulfate, 0.2 g/L; dipotassium phosphate, 0.5 g/L; monopotassium phosphate, 0.5 g/L and calcium chloride, 0.02 g/L. 10 mL of trace element solution was added to one litter of inorganic medium. The composition of trace element solution (g/L) was ferrous sulfate, 0.3 g/L; manganese sulfate, 0.05 g/L; cobalt chloride, 0.1 g/L; sodium molybdate, 0.034 g/L; zinc sulfate, 0.04 g/Land copper sulfate, 0.05 g/L [16]. 4-CP with the concentration of 500 mg/L was initially added to the mediafor carbon source, and the pH of the media was maintained to 7.4. The subculturing of bacterium was carried out after 1 d of interval to the similar medium, which was supplemented with 1g/L of 4-CP. The bacterial cells (OD

_{600 nm}≈ 0.1) were centrifuged after the overnight growth and repeatedly washed with phosphate buffer saline solution (pH 7.4). The centrifugation was performed for precipitation of bacteria, which were used for alginate bead preparation.

### 2.3. Preparation of Ca-alginate Beads Immobilized with Bacterial Cell

_{2}solution (5%) with continuous stirring. Subsequently, bead with different spherical size and shape were formed upon contact between sodium alginate drops and calcium chloride solution. The calcium alginate beads immobilzed with

*B. subtilis MF447840.1*were kept in CaCl

_{2}solution and washed with distilled water. The beads were kept at 4°C for 12 h.

### 2.4. Analytical Procedures

_{600}) to compute the biomass weight from optical densities (OD

_{600}) of the broth culture [16]. The residual 4-CP was measured by taking the absorbance of filtrate at 298 nm achieved after centrifugation of broth for 10 min at 10,000 g, and followed by filtration through 0.22-μm filter [9, 16, 17].

### 2.5. Experiment

_{Ab}(kg mol/m

^{3}) = concentration of 4-chlorophenol in the bulk liquid phase, C

_{As}(kg mol/m

^{3}) = concentration of 4-chlorophenol on the immobilized catalyzed surface, k (m/s) = mass transfer coefficient and N

_{A}(kg mol/m

^{2}·s) = flux rate of 4-chlorophenol.

^{3}), and D

_{AB}is diffusivity of 4-CP (m

^{2}/s). X

_{A1}and X

_{A2}are mole fraction of 4-CP in bulk and immobilized catalyzed surface, respectively. The reaction is considered as an instantaneous; therefore, x

_{A2}= 0, as no A can exist next to the surface of catalyst.

*Φ*is thiele modulus.

*k*and

*a*are reaction rate constant (s

^{−1}) and catalytic surface per unit volume, respectively (m

^{2}/m

^{−3}).

*D*

*and Rare Diffusivity of 4-CP (m*

_{A}^{2}/s) and radius of catalyst (m).

#### 2.5.1. General equation of packed bed

### 2.5.1.1. Laminar flow region

_{a}= average velocity of the fluid, (m/s).

##### (6)

$$\mathrm{\Delta}P/L=\left[150\hspace{0.17em}\mu \hspace{0.17em}{V}_{0}/{{\mathrm{\Phi}}_{s}}^{2}{{D}_{p}}^{2}\right]\u200a\left[{\left(1-\varepsilon \right)}^{2}/{\varepsilon}^{3}\right]$$_{s}= sphericity of the immobilized catalyst bed, D

_{p}= catalyst particle diameter(m); V

_{0}= superficial or empty tower velocity( m/s) and ɛ = void fraction of the bed. The Kozeny-Carman equation specifies that the flow of fluid is proportional to the pressure drop inside PBR and inversely related with the viscosity of fluid, which is equivalent to Ohm’s law, i.e., V

_{c}= IR. This statement is given by Darcy’s law given by Eq. (7) [22].

_{0}= flow velocity, V

_{c}= voltage = ΔP, R = resistance = 1/μ. Burke-Plummer equation is an empirical correlation for the pressure drop in a packed bed at a high Reynolds number (Re

_{p}> 1000) and given by Eq. (8) [22].

##### (8)

$$\mathrm{\Delta}P/L=\left[1.75\hspace{0.17em}\rho \hspace{0.17em}{{V}_{0}}^{2}/{\mathrm{\Phi}}_{s}{D}_{p}\right]\u200a\left[(1\mathrm{\hspace{0.17em}\u200a\u200a}?\mathrm{\hspace{0.17em}\u200a\u200a}\varepsilon )/{\varepsilon}^{3}\right]$$##### (9)

$$\mathrm{\Delta}P/L=\left[150\hspace{0.17em}\mu \hspace{0.17em}{V}_{0}/{{\mathrm{\Phi}}_{s}}^{2}{{D}_{p}}^{2}\right]\u200a\left[{\left(1-\varepsilon \right)}^{2}/{\varepsilon}^{3}\right]+\left[1.75\hspace{0.17em}\rho \hspace{0.17em}{{V}_{0}}^{2}/{\mathrm{\Phi}}_{s}{D}_{p}\right]\u200a\left[\left(1-\varepsilon \right)/{\varepsilon}^{3}\right]$$### 2.6. CFD Analysis

#### 2.6.1. Model for the packed bed reactor

_{0}= V.

##### (10)

$${s}_{i}=-\left[\left(\mu /\alpha \right)\mathrm{\hspace{0.17em}\u200a\u200a}\left({v}_{i}\right)+{{c}_{2}}^{{\scriptstyle \frac{1}{2}}}\rho \hspace{0.17em}\mid v\mid \hspace{0.17em}{v}_{i}\right]$$_{i}is called the source term. The magnitude of the velocity is expressed with |v|. The permeability is expressed with α, and the inertial resistance parameter is expressed with c

_{2}. It indicates simply specify D and C at diagonal matrices with 1/α and c

_{2}, respectively, on the diagonals (and zero for the other elements). Darcy’s law can be expressed by Eq. (11) in porous media.

##### (11)

$$\mathrm{\Delta}P=\left[-\mu /\alpha \right]\left[{V}_{0}\right]=\left[-\mu /\alpha \right]\left[V\right]$$##### (12)

$$\alpha =\left[{{D}_{p}}^{2}/150\right]\u200a\left[{\varepsilon}^{3}/{\left(1\mathrm{\hspace{0.17em}\u200a\u200a}?\mathrm{\hspace{0.17em}\u200a\u200a}\varepsilon \right)}^{2}\right]$$_{p}are viscosity and mean particle diameter, respectively. L and ɛ are abed length and void fraction, respectively.

#### 2.6.2. Inertial losses at porous media

_{2}(in Eq. (10)) at higher velocities modifies for inertial losses inside the porous medium. This constant can be observed as a loss coefficient per unit length alongside the direction of flow. Therefore, the pressure drop is identified as a function of the dynamic head. If modelling of a perforated plate or tube is carried out, the elimination of permeability term can be done sometimes. In that case, the inertial loss term [24] will be used alone and a simplified equation for porous media will be developed (Eq. (13))

_{2}.

*V*and ρ are the velocity and density of the fluid. The magnitude of the velocity is expressed with |v|. c

_{2}is given by Eq. (14).

##### (14)

$${c}_{2}=\left[3.5/{D}_{p}\right]\u200a\left[\left(1-\varepsilon \right)/{\varepsilon}^{3}\right]$$_{2}is specified the coefficient for inertial resistance.

#### 2.6.3. Boundary condition

_{s}= 1) [25] and equal void fraction of bed (porosity is the same for identical particle size). Since fluid velocity was very less; therefore, fluid behavior inside PBR is considered as the laminar and viscous laminar porous pressure-based model is used in this present study. Gambit software was used for designing of PBR having a radius of 0.0075 m and a height of 0.18 m. The wastewater used in this study was considered as Newtonian incompressible isothermal fluid. The fluid is considered a single phase as solute 4-CP concentration is considered to be low, i.e., dilute concentration.

#### 2.6.4. Governing equation

### 2.6.4.1. Equation for continuity or mass balance

##### (16)

$$=\text{i\hspace{0.17em}}(\partial /\partial \text{x})+\text{j\hspace{0.17em}}(\partial /\partial \text{y})+\text{k\hspace{0.17em}}(\partial /\partial \text{z})$$### 2.6.4.2. Momentum balance equation

##### (18)

$$\partial {\text{C}}_{\text{A}}/\partial \text{t}+(\mathbf{u}\xb7\nabla \hspace{0.17em}{\text{C}}_{\text{A}})-{\text{D}}_{\text{A}}{\nabla}^{2}{\text{C}}_{\text{A}}={\text{R}}_{\text{A}}$$_{A}/∂t = 0 as steady-state assumption. Bulk flow term is neglected (

**u**= 0) as dilute solutions were used in the present study. Therefore, the second part of Eq. (17) is zero. For the first-order reaction of A where A becomes exhausted, therefore, R

_{A}= −kC

_{A}kg mol/s·m

^{3}and yields for steady-state are D

_{A}∂

^{2}C

_{A}/∂z

^{2}= kC

_{A}.

### 3. Results and Discussion

### 3.1. Optimization of 4-CP Biodegradation in PBR

*B. subtilis MF447840.1*can able to degrade 4-CP up to a concentration of 1,000 mg/L; however, the specific degradation rate was found to decrease from 500 mg/L to 1,000 mg/L [16]. To understand the role of bed porosity on the degradation of 4-CP in PBR, various alginate bead (2, 4 and 6 cm) were used in PBR and percentage of 4-CP degradation was measured. During these experiments, inlet concentration, bed height, and flow rate were fixed at 500 mg/L, 18 cm and 4 mL/min, respectively. Fig. 2(d) depicts that the degradation of 4-CP is increased with enhanced porosity from 0.24 to 0.375. However, further enhancement of porosity decreases the 4-CP degradation in PBR. The enhancement of porosity from 0.24 to 0.375, decreases pressure drop inside the PBR. It also augments the residence time of fluid in PBR. The residence time of PBR was measured as 3.4 and 5 min for 0.24 and 0.375 of porosity, respectively. Therefore, higher contact time (5 min) between 4-CP and

*B. subtilis MF447840.1*is found in 0.375 of porosity of packed bed, which elevates the degradation of 4-CP. The enhancement of porosity from 0.375 to 0.49 of bed decreases the conversion of 4-CP in PBR, which may be due to reducing of contact time between substrate and catalyst, although, the residence time of PBR is increased to 7 min in the presence of 0.49 of porosity of bed [28]. The present finding states that maximum degradation of 4-CP (99.23%) is found in PBR in 18 cm of bed height, 4 mL/min of flow rate, 500 mg/L of inlet concentration and 0.375 of porosity which conditions are considered as optimum for 4-CP degradation in PBR.

### 3.2. Grid Optimization Test

^{−3}for continuity and 10

^{−5}for momentum). In this case, the fine grid is optimal due to accuracy and stability.

### 3.3. CFD Analysis

^{−5}for all residuals except that of the transport equation, in which the residual was set to 10

^{−3}. The contour plot of the pressure drop, friction factor, and concentration profile was performed.

### 3.4. Mass Transfer Study

### 3.5. Hydrodynamics Study

### 3.6. Validation

### 4. Conclusions

Experiments were carried out to evaluate the optimum condition of bed height, flow rate, inlet concentration of 4-CP, and porosity of bed for maximum degradation of 4-CP in immobilized catalyzed packed bed reactors.

A CFD model was developed to visualize the mass transfer and hydrodynamics of the 4-CP containing wastewater inside the bed using the ANSYS Fluent software and also to predict the optimal condition required for 4-CP degradation in PBR.

Results obtained from both experiments and CFD model show that the percentage of 4-CP degradation depends on the bed height, flow rate, inlet concentration of 4-CP, and porosity of bed. Furthermore, the values of static pressure along with pressure coefficients are higher at the inlet of PBR in compare with the outlet of the bed.

The wall shear stress, strain rate, velocity, and velocity vectors of fluid inside PBR are easily visualized through CFD analysis. CFD analysis shows that the shear stress and strain rates are higher near the wall of PBR than the center of the reactor, which is due to the variation of the velocity of the fluid in center and wall side of PBR. It is also observed that the values of velocity magnitude and velocity vectors are lower in the wall side of the reactor compared to the center of the bed.

The greater mass transfer and faster reaction are found in PBR at the optimized 4 ml/min of flow rate, 18 cm of bed height, 500 mg/L of inlet concentration of 4-CP, and 0.375 of porosity of catalyst bed. This is because of the greater contact time and available contact area for mass transfer and reaction inside PBR.

The experimental and CFD results are well matched with experimental data as a p-value of data obtained from experiments, and the CFD model is within 0.05.